Locally covariant description of a π-meson field
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The algebra of canonical commutation relations is constructed in the Weyl form and a locally covariant formulation of a charged scalar field is presented in terms of the covariant functor. The symplectic space of solutions of the Klein-Gordon-Fock equation is represented as a direct sum of symplectic spaces of positively and negatively charged π mesons. In each of the spaces, these fields satisfy the conditions of the locally covariant quantum field theory. Using natural transformation, the equivalence of two functors describing the π+ and π− mesons is shown. From the physical viewpoint, the equivalence corresponds to the equality of the mesons’ masses.
KeywordsIsometric Embedding Covariant Functor Cauchy Surface Symplectic Space Hyperbolic Space Time
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